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H2SO4 + K2Cr2O7 + [Cr(NH2CONH2)6]3[Cr(CN)6]2 = H2O + CO2 + K2SO4 + Cr2(SO4)3 + KNO3

Input interpretation

H_2SO_4 sulfuric acid + K_2Cr_2O_7 potassium dichromate + (Cr(NH2CONH2)6)3(Cr(CN)6)2 ⟶ H_2O water + CO_2 carbon dioxide + K_2SO_4 potassium sulfate + Cr_2(SO_4)_3 chromium sulfate + KNO_3 potassium nitrate
H_2SO_4 sulfuric acid + K_2Cr_2O_7 potassium dichromate + (Cr(NH2CONH2)6)3(Cr(CN)6)2 ⟶ H_2O water + CO_2 carbon dioxide + K_2SO_4 potassium sulfate + Cr_2(SO_4)_3 chromium sulfate + KNO_3 potassium nitrate

Balanced equation

Balance the chemical equation algebraically: H_2SO_4 + K_2Cr_2O_7 + (Cr(NH2CONH2)6)3(Cr(CN)6)2 ⟶ H_2O + CO_2 + K_2SO_4 + Cr_2(SO_4)_3 + KNO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 K_2Cr_2O_7 + c_3 (Cr(NH2CONH2)6)3(Cr(CN)6)2 ⟶ c_4 H_2O + c_5 CO_2 + c_6 K_2SO_4 + c_7 Cr_2(SO_4)_3 + c_8 KNO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Cr, K, N and C: H: | 2 c_1 + 72 c_3 = 2 c_4 O: | 4 c_1 + 7 c_2 + 18 c_3 = c_4 + 2 c_5 + 4 c_6 + 12 c_7 + 3 c_8 S: | c_1 = c_6 + 3 c_7 Cr: | 2 c_2 + 5 c_3 = 2 c_7 K: | 2 c_2 = 2 c_6 + c_8 N: | 48 c_3 = c_8 C: | 30 c_3 = c_5 Since the coefficients are relative quantities and underdetermined, choose a coefficient to set arbitrarily. To keep the coefficients small, the arbitrary value is ordinarily one. For instance, set c_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 515/2 c_2 = 137/2 c_3 = 1 c_4 = 587/2 c_5 = 30 c_6 = 89/2 c_7 = 71 c_8 = 48 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 515 c_2 = 137 c_3 = 2 c_4 = 587 c_5 = 60 c_6 = 89 c_7 = 142 c_8 = 96 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 515 H_2SO_4 + 137 K_2Cr_2O_7 + 2 (Cr(NH2CONH2)6)3(Cr(CN)6)2 ⟶ 587 H_2O + 60 CO_2 + 89 K_2SO_4 + 142 Cr_2(SO_4)_3 + 96 KNO_3
Balance the chemical equation algebraically: H_2SO_4 + K_2Cr_2O_7 + (Cr(NH2CONH2)6)3(Cr(CN)6)2 ⟶ H_2O + CO_2 + K_2SO_4 + Cr_2(SO_4)_3 + KNO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 K_2Cr_2O_7 + c_3 (Cr(NH2CONH2)6)3(Cr(CN)6)2 ⟶ c_4 H_2O + c_5 CO_2 + c_6 K_2SO_4 + c_7 Cr_2(SO_4)_3 + c_8 KNO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Cr, K, N and C: H: | 2 c_1 + 72 c_3 = 2 c_4 O: | 4 c_1 + 7 c_2 + 18 c_3 = c_4 + 2 c_5 + 4 c_6 + 12 c_7 + 3 c_8 S: | c_1 = c_6 + 3 c_7 Cr: | 2 c_2 + 5 c_3 = 2 c_7 K: | 2 c_2 = 2 c_6 + c_8 N: | 48 c_3 = c_8 C: | 30 c_3 = c_5 Since the coefficients are relative quantities and underdetermined, choose a coefficient to set arbitrarily. To keep the coefficients small, the arbitrary value is ordinarily one. For instance, set c_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 515/2 c_2 = 137/2 c_3 = 1 c_4 = 587/2 c_5 = 30 c_6 = 89/2 c_7 = 71 c_8 = 48 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 515 c_2 = 137 c_3 = 2 c_4 = 587 c_5 = 60 c_6 = 89 c_7 = 142 c_8 = 96 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 515 H_2SO_4 + 137 K_2Cr_2O_7 + 2 (Cr(NH2CONH2)6)3(Cr(CN)6)2 ⟶ 587 H_2O + 60 CO_2 + 89 K_2SO_4 + 142 Cr_2(SO_4)_3 + 96 KNO_3

Structures

+ + (Cr(NH2CONH2)6)3(Cr(CN)6)2 ⟶ + + + +
+ + (Cr(NH2CONH2)6)3(Cr(CN)6)2 ⟶ + + + +

Names

sulfuric acid + potassium dichromate + (Cr(NH2CONH2)6)3(Cr(CN)6)2 ⟶ water + carbon dioxide + potassium sulfate + chromium sulfate + potassium nitrate
sulfuric acid + potassium dichromate + (Cr(NH2CONH2)6)3(Cr(CN)6)2 ⟶ water + carbon dioxide + potassium sulfate + chromium sulfate + potassium nitrate

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2SO_4 + K_2Cr_2O_7 + (Cr(NH2CONH2)6)3(Cr(CN)6)2 ⟶ H_2O + CO_2 + K_2SO_4 + Cr_2(SO_4)_3 + KNO_3 Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the activity expression for each chemical species. • Use the activity expressions to build the equilibrium constant expression. Write the balanced chemical equation: 515 H_2SO_4 + 137 K_2Cr_2O_7 + 2 (Cr(NH2CONH2)6)3(Cr(CN)6)2 ⟶ 587 H_2O + 60 CO_2 + 89 K_2SO_4 + 142 Cr_2(SO_4)_3 + 96 KNO_3 Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i H_2SO_4 | 515 | -515 K_2Cr_2O_7 | 137 | -137 (Cr(NH2CONH2)6)3(Cr(CN)6)2 | 2 | -2 H_2O | 587 | 587 CO_2 | 60 | 60 K_2SO_4 | 89 | 89 Cr_2(SO_4)_3 | 142 | 142 KNO_3 | 96 | 96 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 515 | -515 | ([H2SO4])^(-515) K_2Cr_2O_7 | 137 | -137 | ([K2Cr2O7])^(-137) (Cr(NH2CONH2)6)3(Cr(CN)6)2 | 2 | -2 | ([(Cr(NH2CONH2)6)3(Cr(CN)6)2])^(-2) H_2O | 587 | 587 | ([H2O])^587 CO_2 | 60 | 60 | ([CO2])^60 K_2SO_4 | 89 | 89 | ([K2SO4])^89 Cr_2(SO_4)_3 | 142 | 142 | ([Cr2(SO4)3])^142 KNO_3 | 96 | 96 | ([KNO3])^96 The equilibrium constant symbol in the concentration basis is: K_c Mulitply the activity expressions to arrive at the K_c expression: Answer: | | K_c = ([H2SO4])^(-515) ([K2Cr2O7])^(-137) ([(Cr(NH2CONH2)6)3(Cr(CN)6)2])^(-2) ([H2O])^587 ([CO2])^60 ([K2SO4])^89 ([Cr2(SO4)3])^142 ([KNO3])^96 = (([H2O])^587 ([CO2])^60 ([K2SO4])^89 ([Cr2(SO4)3])^142 ([KNO3])^96)/(([H2SO4])^515 ([K2Cr2O7])^137 ([(Cr(NH2CONH2)6)3(Cr(CN)6)2])^2)
Construct the equilibrium constant, K, expression for: H_2SO_4 + K_2Cr_2O_7 + (Cr(NH2CONH2)6)3(Cr(CN)6)2 ⟶ H_2O + CO_2 + K_2SO_4 + Cr_2(SO_4)_3 + KNO_3 Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the activity expression for each chemical species. • Use the activity expressions to build the equilibrium constant expression. Write the balanced chemical equation: 515 H_2SO_4 + 137 K_2Cr_2O_7 + 2 (Cr(NH2CONH2)6)3(Cr(CN)6)2 ⟶ 587 H_2O + 60 CO_2 + 89 K_2SO_4 + 142 Cr_2(SO_4)_3 + 96 KNO_3 Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i H_2SO_4 | 515 | -515 K_2Cr_2O_7 | 137 | -137 (Cr(NH2CONH2)6)3(Cr(CN)6)2 | 2 | -2 H_2O | 587 | 587 CO_2 | 60 | 60 K_2SO_4 | 89 | 89 Cr_2(SO_4)_3 | 142 | 142 KNO_3 | 96 | 96 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 515 | -515 | ([H2SO4])^(-515) K_2Cr_2O_7 | 137 | -137 | ([K2Cr2O7])^(-137) (Cr(NH2CONH2)6)3(Cr(CN)6)2 | 2 | -2 | ([(Cr(NH2CONH2)6)3(Cr(CN)6)2])^(-2) H_2O | 587 | 587 | ([H2O])^587 CO_2 | 60 | 60 | ([CO2])^60 K_2SO_4 | 89 | 89 | ([K2SO4])^89 Cr_2(SO_4)_3 | 142 | 142 | ([Cr2(SO4)3])^142 KNO_3 | 96 | 96 | ([KNO3])^96 The equilibrium constant symbol in the concentration basis is: K_c Mulitply the activity expressions to arrive at the K_c expression: Answer: | | K_c = ([H2SO4])^(-515) ([K2Cr2O7])^(-137) ([(Cr(NH2CONH2)6)3(Cr(CN)6)2])^(-2) ([H2O])^587 ([CO2])^60 ([K2SO4])^89 ([Cr2(SO4)3])^142 ([KNO3])^96 = (([H2O])^587 ([CO2])^60 ([K2SO4])^89 ([Cr2(SO4)3])^142 ([KNO3])^96)/(([H2SO4])^515 ([K2Cr2O7])^137 ([(Cr(NH2CONH2)6)3(Cr(CN)6)2])^2)

Rate of reaction

Construct the rate of reaction expression for: H_2SO_4 + K_2Cr_2O_7 + (Cr(NH2CONH2)6)3(Cr(CN)6)2 ⟶ H_2O + CO_2 + K_2SO_4 + Cr_2(SO_4)_3 + KNO_3 Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the rate term for each chemical species. • Write the rate of reaction expression. Write the balanced chemical equation: 515 H_2SO_4 + 137 K_2Cr_2O_7 + 2 (Cr(NH2CONH2)6)3(Cr(CN)6)2 ⟶ 587 H_2O + 60 CO_2 + 89 K_2SO_4 + 142 Cr_2(SO_4)_3 + 96 KNO_3 Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i H_2SO_4 | 515 | -515 K_2Cr_2O_7 | 137 | -137 (Cr(NH2CONH2)6)3(Cr(CN)6)2 | 2 | -2 H_2O | 587 | 587 CO_2 | 60 | 60 K_2SO_4 | 89 | 89 Cr_2(SO_4)_3 | 142 | 142 KNO_3 | 96 | 96 The rate term for each chemical species, B_i, is 1/ν_i(Δ[B_i])/(Δt) where [B_i] is the amount concentration and t is time: chemical species | c_i | ν_i | rate term H_2SO_4 | 515 | -515 | -1/515 (Δ[H2SO4])/(Δt) K_2Cr_2O_7 | 137 | -137 | -1/137 (Δ[K2Cr2O7])/(Δt) (Cr(NH2CONH2)6)3(Cr(CN)6)2 | 2 | -2 | -1/2 (Δ[(Cr(NH2CONH2)6)3(Cr(CN)6)2])/(Δt) H_2O | 587 | 587 | 1/587 (Δ[H2O])/(Δt) CO_2 | 60 | 60 | 1/60 (Δ[CO2])/(Δt) K_2SO_4 | 89 | 89 | 1/89 (Δ[K2SO4])/(Δt) Cr_2(SO_4)_3 | 142 | 142 | 1/142 (Δ[Cr2(SO4)3])/(Δt) KNO_3 | 96 | 96 | 1/96 (Δ[KNO3])/(Δt) (for infinitesimal rate of change, replace Δ with d) Set the rate terms equal to each other to arrive at the rate expression: Answer: | | rate = -1/515 (Δ[H2SO4])/(Δt) = -1/137 (Δ[K2Cr2O7])/(Δt) = -1/2 (Δ[(Cr(NH2CONH2)6)3(Cr(CN)6)2])/(Δt) = 1/587 (Δ[H2O])/(Δt) = 1/60 (Δ[CO2])/(Δt) = 1/89 (Δ[K2SO4])/(Δt) = 1/142 (Δ[Cr2(SO4)3])/(Δt) = 1/96 (Δ[KNO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2SO_4 + K_2Cr_2O_7 + (Cr(NH2CONH2)6)3(Cr(CN)6)2 ⟶ H_2O + CO_2 + K_2SO_4 + Cr_2(SO_4)_3 + KNO_3 Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the rate term for each chemical species. • Write the rate of reaction expression. Write the balanced chemical equation: 515 H_2SO_4 + 137 K_2Cr_2O_7 + 2 (Cr(NH2CONH2)6)3(Cr(CN)6)2 ⟶ 587 H_2O + 60 CO_2 + 89 K_2SO_4 + 142 Cr_2(SO_4)_3 + 96 KNO_3 Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i H_2SO_4 | 515 | -515 K_2Cr_2O_7 | 137 | -137 (Cr(NH2CONH2)6)3(Cr(CN)6)2 | 2 | -2 H_2O | 587 | 587 CO_2 | 60 | 60 K_2SO_4 | 89 | 89 Cr_2(SO_4)_3 | 142 | 142 KNO_3 | 96 | 96 The rate term for each chemical species, B_i, is 1/ν_i(Δ[B_i])/(Δt) where [B_i] is the amount concentration and t is time: chemical species | c_i | ν_i | rate term H_2SO_4 | 515 | -515 | -1/515 (Δ[H2SO4])/(Δt) K_2Cr_2O_7 | 137 | -137 | -1/137 (Δ[K2Cr2O7])/(Δt) (Cr(NH2CONH2)6)3(Cr(CN)6)2 | 2 | -2 | -1/2 (Δ[(Cr(NH2CONH2)6)3(Cr(CN)6)2])/(Δt) H_2O | 587 | 587 | 1/587 (Δ[H2O])/(Δt) CO_2 | 60 | 60 | 1/60 (Δ[CO2])/(Δt) K_2SO_4 | 89 | 89 | 1/89 (Δ[K2SO4])/(Δt) Cr_2(SO_4)_3 | 142 | 142 | 1/142 (Δ[Cr2(SO4)3])/(Δt) KNO_3 | 96 | 96 | 1/96 (Δ[KNO3])/(Δt) (for infinitesimal rate of change, replace Δ with d) Set the rate terms equal to each other to arrive at the rate expression: Answer: | | rate = -1/515 (Δ[H2SO4])/(Δt) = -1/137 (Δ[K2Cr2O7])/(Δt) = -1/2 (Δ[(Cr(NH2CONH2)6)3(Cr(CN)6)2])/(Δt) = 1/587 (Δ[H2O])/(Δt) = 1/60 (Δ[CO2])/(Δt) = 1/89 (Δ[K2SO4])/(Δt) = 1/142 (Δ[Cr2(SO4)3])/(Δt) = 1/96 (Δ[KNO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| sulfuric acid | potassium dichromate | (Cr(NH2CONH2)6)3(Cr(CN)6)2 | water | carbon dioxide | potassium sulfate | chromium sulfate | potassium nitrate formula | H_2SO_4 | K_2Cr_2O_7 | (Cr(NH2CONH2)6)3(Cr(CN)6)2 | H_2O | CO_2 | K_2SO_4 | Cr_2(SO_4)_3 | KNO_3 Hill formula | H_2O_4S | Cr_2K_2O_7 | C30H72Cr5N48O18 | H_2O | CO_2 | K_2O_4S | Cr_2O_12S_3 | KNO_3 name | sulfuric acid | potassium dichromate | | water | carbon dioxide | potassium sulfate | chromium sulfate | potassium nitrate IUPAC name | sulfuric acid | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | | water | carbon dioxide | dipotassium sulfate | chromium(+3) cation trisulfate | potassium nitrate
| sulfuric acid | potassium dichromate | (Cr(NH2CONH2)6)3(Cr(CN)6)2 | water | carbon dioxide | potassium sulfate | chromium sulfate | potassium nitrate formula | H_2SO_4 | K_2Cr_2O_7 | (Cr(NH2CONH2)6)3(Cr(CN)6)2 | H_2O | CO_2 | K_2SO_4 | Cr_2(SO_4)_3 | KNO_3 Hill formula | H_2O_4S | Cr_2K_2O_7 | C30H72Cr5N48O18 | H_2O | CO_2 | K_2O_4S | Cr_2O_12S_3 | KNO_3 name | sulfuric acid | potassium dichromate | | water | carbon dioxide | potassium sulfate | chromium sulfate | potassium nitrate IUPAC name | sulfuric acid | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | | water | carbon dioxide | dipotassium sulfate | chromium(+3) cation trisulfate | potassium nitrate

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